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Grade 12Algebra

Let R be the set of real numbers, f : R?R be the function defined by f (x) = 4x + 3, x ? R. Show that f is invertible. Find the inverse of f ?

sudhanshu

12 Years agoGrade 12

1 Answer

Jitender Singh

12 Years ago

Ans:

$f : R\rightarrow R$

$f(x) = 4x + 3$

Since range of function is equal to co-domain, so it is onto function.

It is straight line, so it is clear from the graph that it is one to one function.

-> f(x) is bijective function, so it can be invertible.

$x\rightarrow f^{-1}(x)$

$f(f^{-1}(x)) = 4f^{-1}(x) + 3$

$f(f^{-1}(x)) = x$

$f^{-1}(x) = \frac{x-3}{4}$

Thanks & Regards

Jitender Singh

IIT Delhi

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